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Bipartitional polynomials and their applications in combinatorics and statistics

Ch.A. Charalambides
1981 Discrete Mathematics  
Recurrence relations, generating functions and some basic properties or these polynomials are given. Applications in Combinatorics and Statistics are briefiy indicated..  ...  Bipartitional polynomials are multivariable polynomials Y ,",*=Ynln(CYOI~CYlorCY,I~..-rCYlnn)r Ck'Ck, defined by a sum over ail partitions of the bpartite number (mn).  ...  Riordan [6, 7] called Bell polynomials the partition polynomials associated with the derivatives of a composite function; he discussed several applications of these polynomials in Combinatorics, Statistics  ... 
doi:10.1016/0012-365x(81)90024-8 fatcat:viu6mybgnbc3nkqu2xge7v4cse

Page 1390 of Mathematical Reviews Vol. , Issue 82d [page]

1982 Mathematical Reviews  
A. 82d:05010 Bipartitional polynomials and their applications in combinatorics and statistics. Discrete Math. 34 (1981), no. 1, 81-84.  ...  Recurrence relations, generalizing functions and some basic properties of these 82d:05009 1390 polynomials are given. Applications in combinatorics and statistics are briefly indicated.”  ... 

Page 6447 of Mathematical Reviews Vol. , Issue 96k [page]

1996 Mathematical Reviews  
He remarks that rational series are probably not well known in combinatorics, although their one-variable version (linear recursive sequences) is certainly well known.  ...  Some new enumeration results for semiregular bipartite graphs are included, and the related cat- egory of the quasi-semiregular bipartite graphs is recognized.  ... 

Page 820 of Mathematical Reviews Vol. , Issue 2002B [page]

2002 Mathematical Reviews  
(English summary) Special issue on design combinatorics: in honor of S. S. Shrikhande. J. Statist. Plann. Inference 95 (2001), no. 1-2, 197-208.  ...  Concentration of multivariate polynomials and its applications. (English summary) Combinatorica 20 (2000), no. 3, 417-434. Let f = f(x),...  ... 

Page 1553 of Mathematical Reviews Vol. , Issue 2002C [page]

2002 Mathematical Reviews  
[Zhu, Lie'] (PRC-SOO; Suzhou) V (m, ¢) and its variants. (English summary) Special issue on design combinatorics: in honor of S.S. Shrikhande. J. Statist. Plann.  ...  The algorithm runs in time polynomial in the size of V’ and V°. This algorithm can be used to obtain a polynomial time algorithm for finding an unbalanced hole in a graph that contains one.  ... 

Discrete mathematics: methods and challenges [article]

Noga Alon
2002 arXiv   pre-print
Combinatorics is a fundamental mathematical discipline as well as an essential component of many mathematical areas, and its study has experienced an impressive growth in recent years.  ...  This is a survey of two of the main general techniques that played a crucial role in the development of modern combinatorics; algebraic methods and probabilistic methods.  ...  These include applications in Information Theory and Electrical Engineering, in Statistical Physics, in Chemistry and Molecular Biology, and, of course, in Computer Science.  ... 
arXiv:math/0212390v1 fatcat:v4iw43rdzbgjroxo37nsl45nle

Page 7177 of Mathematical Reviews Vol. , Issue 95m [page]

1995 Mathematical Reviews  
These combinatorial problems have their origins in statistical mechanics.”  ...  (English summary) Combinatorics, graph theory, algorithms and applications ( Beijing, 1993), 17-20, World Sci. Publishing, River Edge, NJ, 1994.  ... 

Page 4539 of Mathematical Reviews Vol. , Issue 91H [page]

1991 Mathematical Reviews  
(H-AOS-C) Polynomial algorithms for finding cycles and paths in bipartite tournaments. SIAM J. Discrete Math. 3 (1990), no. 4, 537-543.  ...  This paper presents algorithms for determining the existence of specific paths and cycles in a bipartite tournament (a complete directed bipartite graph).  ... 

Page 918 of Mathematical Reviews Vol. , Issue 83c [page]

1983 Mathematical Reviews  
Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978). Ann.  ...  . * Combinatorics and graph theory. 83c:05002 Proceedings of the Second Symposium held at the Indian Statistical © Institute, Calcutta, February 25-29, 1980. Edited by Siddani Bhaskara Rao.  ... 

Page 4954 of Mathematical Reviews Vol. , Issue 99g [page]

1999 Mathematical Reviews  
Using the combinatorics of biwords (words over biletters) it is shown here how four such transformations that have occurred in earlier work by the authors and their collabo- rators [P. Cartier and D.  ...  We present polynomial time algorithms of two different types. Algorithms of the first type always run in polynomial time and succeed almost surely. A. L. Blum and J. H. Spencer [J.  ... 

Page 7575 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
From the introduction: “Hall-Litthkewood functions are known to be related to a variety of topics in representation theory, geome- try and combinatorics.  ...  We present a series of conjectures on these new functions, and prove them in the two extreme cases: for the shortest possible ribbons (dominoes), OSE Algebraic combinatorics and for sufficiently long ones  ... 

Recent Developments in Extremal Combinatorics: Ramsey and Turán Type Problems

Benny Sudakov
2011 Proceedings of the International Congress of Mathematicians 2010 (ICM 2010)  
In this paper we discuss some recent advances in this subject, focusing on two topics which played an important role in the development of extremal combinatorics: Ramsey and Turán type questions for graphs  ...  Extremal combinatorics is one of the central branches of discrete mathematics and has experienced an impressive growth during the last few decades.  ...  Acknowledgments I would like to thank Conlon, Fox, Keevash, Krivelevich and Markman for carefully reading this manuscript and many valuable comments, which greatly improved the presentation.  ... 
doi:10.1142/9789814324359_0159 fatcat:6dzzmc7s3bbufe36nr3k7mh5vi

Subset Glauber Dynamics on Graphs, Hypergraphs and Matroids of Bounded Tree-Width

Magnus Bordewich, Ross J. Kang
2014 Electronic Journal of Combinatorics  
mixing for the Tutte polynomial, adjacency-rank ($R_2$-)polynomial and interlace polynomial.  ...  In particular Glauber dynamics for the $R_2$-polynomial was known to mix rapidly on trees, which led to hope of rapid mixing on a wider class of graphs.  ...  , and statistics.  ... 
doi:10.37236/4195 fatcat:amjdhchrdzfs3leyuavc3uhgaa

Page 2283 of Mathematical Reviews Vol. , Issue 83f [page]

1983 Mathematical Reviews  
Their treatment requires some number-theoretic preparation in which regular partitions of Z, are defined and their existence established in many cases.” de Caen, D.; Gregory, D. A.; Pullman, N. J.  ...  Barlotti, Information theory (French) (Cachan, 1977), pp. 185-187, CNRS, Paris, 1978; see MR 8le:94001], and the study of the packing problem for these sets turns out to be natural and interesting in applications  ... 

Page 2298 of Mathematical Reviews Vol. , Issue 87e [page]

1987 Mathematical Reviews  
Akiyama and M. Kano. In this note it is shown that both complete bipartite graphs K(2n—1,2n—1) and K(2n, 2n) have star index n +2 (except for some small values of n). H.  ...  He defines a “separation” prop- erty for polynomials (based on the relative locations of their zeros) and shows that this property is enjoyed by polynomials which are formed by linear combinations of the  ... 
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